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					    Systematic challenges in future
      dark energy measurements

John Peacock   Tokyo HSC Workshop   Nov 2006
Working Group
on Fundamental

John Peacock (Chair)
Peter Schneider (Co-Chair)
George Efstathiou
Jonathan R. Ellis
Bruno Leibundgut
Simon Lilly
Yannick Mellier
Major contributors:
Pierre Astier, Anthony Banday,
Hans Boehringer, Anne Ealet,
Martin Haehnelt, Guenther
Hasinger, Paolo Molaro, Jean-
Loup Puget, Bernard Schutz,
Uros Seljak, Jean-Philippe Uzan
Dark Energy
Task Force

 Report to NSF,

   Rocky Kolb
  Andy Albrecht
Cosmology: Concordance Model
              Heavy elements 0.03%

              Neutrinos 0.3%

              Stars 0.5%

              H + He gas 4%

              Dark matter 20%

              Dark Energy 75%

                    Outstanding questions:
                    • initial conditions (inflation?)
                    • nature of the dark matter
                    • nature of the dark energy
        The cosmological parameters
  Only 6 parameters needed (flat; no gravity waves)

                                     Optical depth from reionization
                                     Scalar spectral index
2dFGRS                               Baryon density ( =  h2)
                                     CDM density ( =  h2)
                                     H0 / 100

+ r (tensor fraction), curvature, m , w ´ P/ (DE eqn of state)
            DE is entangled with other parameters
            The nature of dark energy

(1) Zero-point energy?

) expect vac » Emax4 (natural units: c=h=1)
But empirically Emax = 2.4 meV    - not a real cutoff

(2) Dynamical ‘Dark Energy’
-   ‘Quintessence’: use inflationary technology of w<0
    from scalar fields
-   Empirical w= P/ c2 (= -1?); fit w(a) = w0 + wa(1-a)
 Dark Energy: sensitivity
      & degeneracy
Vacuum affects H(z):
H2(z) = H20 [ M (1+z) 3 + R (1+z) 4 + V (1+z) 3 (1+w) ]
               matter        radiation     vacuum

Alters D(z) via r = s c dz / H

And growth via 2H d/dt term in growth equation
                                                             Rule of 5
Both effects are

(1)    Small (need D to 0.2% for w to § 1%)

(2)    Degenerate with changes in m                                     growth

To measure w to a few %, we need to have
independent data on m and to be able to

control systematics to a few parts in 1000

− even harder with lensing (rule of 10)
Dark energy: current status


                      Need to aim
                      for 1%
                      precision in
                      future work
Ruling in L: Bayesian view

           Evidence ratio: trade likelihood ratio against
           how much of parameter space is ruled out

           Trotta (2005): roughly 1% accuracy on w will
           prove it’s L unless we measure a large
           likelihood against that model
    Evolving Dark Energy: pivot redshifts
Assume w = w0 + wa(1-a)
If observe degeneracy w0 = A + Bwa,
) w = A + (B+1-a)wa
) zpivot = 1/(1+B) - 1

       Method            zpivot
       CMB               0.43
       BAO z=1           0.54
                                  Difficult to get much baseline
       BAO z=1+z=3       0.85
       Lensing           0.25
 Not everything
  may fit: new
  physics, or

   − need for

− harder in future
The CMB: common basis for all methods
        CMB degeneracies and w
Comoving distance-redshift relation: ( =  h2)

CMB power spectrum depends only on m and b (apart
from large-scale ISW and reionization)
Thus degeneracy between curvature and vacuum (vary both
to keep D fixed)
Flat case: vary v and w.
Degeneracy broken by large-scale effects. Thus limit on w
from good CMB data alone
     Lensing vs                SNe        vs BAO
      (Dune)                (SNAP)           (WFMOS 5000)

And similar constraints from mass function of 100,000 clusters

DETF likes  w0 £  wa but not so clear – kill L first
Probe 1: Supernovae

 Ground vs HST

                 Standard candles: distances to 5%
                 Currently samples of few hundred
                 Space resolution essential for high z
   Supernovae: Future challenges

 Now: ~500 SNe (SNLS). 2010: ~5,000 (Pan-STARRS)
 Could yield w to 2%, but:
  –   Photometric accuracy to < 1% needed
  –   Malmquist worries at higher z
  –   Contamination by non-Ia
  –   Non-MW extinction
  –   Evolution of these factors, even ignoring intrinsic
Probe 2: Gravitational lensing

Image distortion depends on
− D(z) via baseline
− growth of structure
    Shear Data: Ground vs Space

                                       Typical cosmic
                space                  shear is ~ 1%, and
                                       must be measured
            weak lensing shear         with high accuracy

                                       Even so, 1%
                                       precision on w
                                       needs > 10,000
                                       deg2 surveys

Space: small and stable PSF
 larger number of resolved galaxies
 reduced systematics
            Photometric redshifts

Broad-band data can give z/(1+z) ' 0.04
But expect catastrophic failures for z>1 with optical only
Sufficiently deep near-IR (K ' 22) needs space
       Lensing: future challenges
 PSF correction: STEP testing shows that even
  measuring shear with 1% precision is hard.
 Photo-z precision: need to know <z> in a few
  tomographic z bands to 0.1% fractional accuracy
   – needs >105 z’s to calibrate
 Nonlinear corrections: most observations to date
  probe only shear correlations < 10 arcmin
   – need more accurate models for nonlinear P(k)
   – effect of baryons?
 Intrinsic effects:
   – alignment of close pairs
   – foreground-background alignments
 Probe 3: Clusters of galaxies

Evolving mass function sensitive to g(z)
Apparent baryon fraction depends on D(z)
      Clusters: future challenges

 Projection effects: Need X-ray survey (eROSITA?)
 Mass estimates:
   – Accuracy of mass estimation from X-ray/SZ (8% rms)
   – Self-calibration to avoid bias in masses
 Redshift accuracy:
   – need  z/(1+z) ' 0.02
   – Maybe OK via averaging photo-z’s
   – but needs 105 z’s for calibration in any case
  Probe 4: P(k) and Baryon oscillations

(1) Matter-radiation horizon:
123 (m h2 / 0.13)-1 Mpc
(2) Acoustic horizon at last scattering :
          2         -0.25        2           -0.08
147 (m h / 0.13)           (b h / 0.024)           Mpc

Standard rulers to probe distance-z relation
 BAO: Precision on D(z) and volume
                                           % error in D =
                                           (V / 5 h-3 Gpc3)-1/2
                                           £ (kmax / 0.2 h Mpc-1)-1/2

 0.7 < z < 1.3: 1 (h-1Gpc)3 = 540 deg2
 2.5 < z < 3.5 : 1 (h-1Gpc)3 = 254 deg2

 Thus 1% distance accuracy (5% on w) needs
  2000 (z=1) or 1000 (z=3) deg2
 Really prefer > 5000 deg2 at z = 1 (>5 million z’s)
  z = 3 selection problematic
BAO with Photo-z’s

    Schuecker   Much less efficient:
                e.g. ESO VST/KIDS, 60
                million photo-z over 1500
                deg2 gives 14% predicted
                error on w:
                ~100 times bigger sample
                needed for same accuracy
                as WFMOS
                Possibly interesting with
                all-sky data, but demanding
                on photometric uniformity

Need to show that acoustic scale is at linear prediction to
few parts in 1000
Why might it not be?:
   • Mass nonlinearities
   • Scale-dependent bias
   • Mask convolution
   • Missing close pairs
Needs many semi-realistic mock surveys
Semianalytic galaxies in MS: 1014M¯ halo
  Dark matter              Galaxies
                  Galaxy power:
                  effects at z=3
                   than at z=1

z=7        z=3
           gals     Power spectrum
                  from MS divided by
                     a baryon-free
                    LCDM spectrum
z=1        z=0
                   Springel et al. 2005
Larger volumes: mock galaxy P(k) data

                         Semianalytic data from
                         Durham 1 Gpc/h cube

                             Systematic shift
                               in oscillation
                          scale relative to linear
                             theory of ~1%

                         Can plausibly calibrate
                         this down to 0.1% shift
     1.8m telescope on Haleakala, Maui
     7 deg2 OT CCD camera
     Survey operations from mid-2007
       – Initial programme runs to end 2010
       – 20,000 deg2 grizy to i=23.8
       – 84 deg2 grizy to i=27.0
     Most powerful imaging cosmology data
      prior to DES, HSC
       – Should get w to 2-3% from each of
          lensing, SNe, photo-z BAOs
     Science consortium: Hawaii, MPG
      Germany, CfA, JHU, UK (Belfast,
      Durham, Edinburgh)

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